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It's quite important, because if ownership of external objects can be considered an extension of this idea of "self-ownership" (which seems to exist only to justify the idea of private property) then it can be used as the justification for violence framed as "self-defense."

Ah I understand what you're saying more clearly now. I'll have to think about that.

How do you live without private property? Do you own a house? A computer or smart phone? Clothes? Tools? Or do you live in a cave like a cavemen? Even cavemen had property, the tools made from wood and stone, the food they gathered or hunted, and the cave they lived in...

How do you live without any property?

It's just stuff, really. We don't have to go inventing categories to justify violence.

So, if I picked your pocket to steal from you, you won't feel justified using violence in self defense?